Since the hospital financing is more and more based on a budget in function of the pathologies, it appears necessary to detect hospital stays presenting discrepancy between the resources they used and the medical characteristics they present. We propose the use of deterministic nonparametric frontier models to rank hospital stays in function of their expenses taking into account the severity level of the patient. In this case, the hospital stays with the lowest total expenses for a given level of severity are considered as efficient. But, deterministic models are very sensitive to the extreme stays so that some efficient stays could be in fact ‘too’ efficient and considered as outliers. We try to highlight these stays using the method of Simar (2001) which is based on the concept of order-m frontier. The idea is to define a ‘benchmark’ frontier that doesn’t envelop all the data. Indeed, for a given level of severity, a reasonable minimal value of the expenses is estimated. The hospital stays with expenses lower than this reasonable value could be considered as ‘outlier’ and require further analysis. We compare our results with these obtained in Beguin (2001) which relies on a method proposed by Wilson (1995). As a conclusion, we recommend the use of both methods to detect the outlier and so to obtain a better ranking of the other hospital stays.